Anything in red has been solved. Anything in green has been somewhat solved.
Ok, so I have Windows 7 Ultimate 64 bit, and all of my specs meet the requirements to play Zero Hour, and use the worldbuilder.

Zero Hour:
Problem #1: When I start the game, a background video is supposed to start. It doesn't.
Solution #1: UNKNOWN

Problem #2: Can't go online. I can login, but as soon as it loads, it gives me some error saying that something is corrupt.
Solution#2: I uninstalled the game, and left any remains of it, and installed it again.

Worldbuilder:
Problem: After I've clicked accept and Worldbuilder has opened, I click on something... for say, the smooth tool, it gives me an error, and Worldbuilder freezes if I try using the tool.
Solution: Click ignore as many times as you have to.

Are you running in xp compatibility mode?

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I tried running it in both XP Mode and with my normal Windows 7 Ultimate 64 bit Operating System.

We all get these error messages when clicking on a tool. Click ignore then ignore from now on until it clears. You should be able to use that tool without problems from then on.

Hey, it worked, thanks!

I don't really have a solution for problem #1, but different shell maps play based of the graphic settings of the game that your PC can run. After getting the game started, have you gone to Settings and adjusted for higher quality graphics then Exit/Restart the game?

Yeah, I've already tried that along with a similar possible solution. "Set the settings to be in worse quality, and then restart the game."